AbstractSlipping motions of magnetic field lines are a distinct signature of three-dimensional magnetic reconnection, a fundamental process driving solar and stellar flares. While being a key prediction of numerical experiments, the rapid super-Alfvénic field line slippage driven by the ‘slip-running’ reconnection has remained elusive in previous observations. New frontiers into exploring transient flare phenomena were introduced by recently designed high cadence observing programs of the Interface Region Imaging Spectrograph (IRIS). By exploiting high temporal resolution imagery (~2 s) of IRIS, here we reveal slipping motions of flare kernels at speeds reaching thousands of kilometres per second. The fast kernel motions are direct evidence of slip-running reconnection in quasi-separatrix layers, regions where magnetic field strongly changes its connectivity. Our results provide observational proof of theoretical predictions unaddressed for nearly two decades and extend the range of magnetic field configurations where reconnection-related phenomena can occur.